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# Arcsec sqrt6 + sqrt2

Welcome to arcsec sqrt6 + sqrt2, our post aboutthe arcsecant of sqrt6 + sqrt2.

For the inverse trigonometric function of secant sqrt6 + sqrt2 we usually employ the abbreviation arcsec and write it as arcsec sqrt6 + sqrt2 or arcsec(sqrt6 + sqrt2).

If you have been looking for what is arcsec sqrt6 + sqrt2, either in degrees or radians, or if you have been wondering about the inverse of sec sqrt6 + sqrt2, then you are right here, too.

In this post you can find the angle arcsecant of sqrt6 + sqrt2, along with identities.

Read on to learn all about the arcsec of sqrt6 + sqrt2, and note that the term sqrt6+sqrt2 is approximately 3.863703305 as a decimal number.

## Arcsec of sqrt6 + sqrt2

If you want to know what is arcsec sqrt6 + sqrt2 in terms of trigonometry, check out the explanations in the last paragraph; ahead in this section is the value of arcsecant(sqrt6 + sqrt2):

arcsec sqrt6 + sqrt2 = 5pi/12 rad = 75°
arcsecant sqrt6 + sqrt2 = 5pi/12 rad = 75 °
arcsecant of sqrt6 + sqrt2 = 5pi/12 radians = 75 degrees

The arcsec of sqrt6 + sqrt2 is 5pi/12 radians, and the value in degrees is 75°. To change the result from the unit radian to the unit degree multiply the angle by 180° / $\pi$ and obtain 75°.

Our results above contain fractions of pi for the results in radian, and are exact values otherwise. If you compute arcsec(sqrt6 + sqrt2), and any other angle, using the calculator below, then the value will be rounded to ten decimal places.

To obtain the angle in degrees insert sqrt6 + sqrt2 as decimal in the field labelled “x”. However, if you want to be given the angle of sec sqrt6 + sqrt2 in radians, then you must press the swap units button.

### Calculate arcsec x

Apart from the inverse of sec sqrt6 + sqrt2, similar trigonometric calculations include:

The identities of arcsecant sqrt6 + sqrt2 are as follows: arcsec(sqrt6 + sqrt2) =

• $\frac{\pi}{2}$ – arccsc(sqrt6 + sqrt2) ⇔ 90°- arccsc(sqrt6 + sqrt2)
• $\pi$ – arcsec(-sqrt6 + sqrt2) ⇔ 180° – arcsec(-sqrt6 + sqrt2)
• arccos($\frac{1}{\sqrt{2}+\sqrt{6}}$)

The infinite series of arcsec sqrt6 + sqrt2 is: $\frac{\pi}{2} – \sum_{n=0}^{\infty}\frac{\binom{2n}{n}(\sqrt{2}+\sqrt{6})^{-(2n+1)}}{4^{n}(2n+1)}$.

Next, we discuss the derivative of arcsec sqrt6 + sqrt2 for sqrt6 + sqrt2 = sqrt6 + sqrt2. In the following paragraph you can additionally learn what the search calculations form in the sidebar is used for.

## Derivative of arcsec sqrt6 + sqrt2

The derivative of arcsec sqrt6 + sqrt2 is particularly useful to calculate the inverse secant sqrt6 + sqrt2 as an integral.

The formula for x is (arcsec x)’ = $\frac{1}{|x|\sqrt{x^{2}-1}}$, |x| > 1, so for x = sqrt6 + sqrt2 the derivative equals 0.0693503541.

Using the arcsec sqrt6 + sqrt2 derivative, we can calculate the angle as a definite integral:

arcsec sqrt6 + sqrt2 = $\int_{1}^{\sqrt{2}+\sqrt{6}}\frac{1}{z\sqrt{z^{2}-1}}dz$.

The relationship of arcsec of sqrt6 + sqrt2 and the trigonometric functions sin, cos and tan is:

• sin(arcsecant(sqrt6 + sqrt2)) = $\frac{\sqrt{(\sqrt{2}+\sqrt{6})^{2}-1}}{\sqrt{2}+\sqrt{6}}$
• cos(arcsecant(sqrt6 + sqrt2)) = $\frac{1}{\sqrt{2}+\sqrt{6}}$
• tan(arcsecant(sqrt6 + sqrt2)) = $\sqrt{(\sqrt{2}+\sqrt{6})^{2}-1}$

Note that you can locate many terms including the arcsecant(sqrt6 + sqrt2) value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, arcsecsqrt6 + sqrt2 angle.

Using the aforementioned form in the same way, you can also look up terms including derivative of inverse secant sqrt6 + sqrt2, inverse secant sqrt6 + sqrt2, and derivative of arcsec sqrt6 + sqrt2, just to name a few.

In the next part of this article we discuss the trigonometric significance of arcsecant sqrt6 + sqrt2, and there we also explain the difference between the inverse and the reciprocal of sec sqrt6 + sqrt2.

## What is arcsec sqrt6 + sqrt2?

In a triangle which has one angle of 90 degrees, the cosine of the angle α is the ratio of the length of the adjacent side a to the length of the hypotenuse h: cos α = a/h.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, α is the angle formed by the two sides x and r; r moving counterclockwise defines the positive angle.

As follows from the unit-circle definition on our homepage, assumed r = 1, in the intersection of the point (x,y) and the circle, cos α = x / r = x, and sec α = 1 / x = sqrt6 + sqrt2. The angle whose secant value equals sqrt6 + sqrt2 is α.

In the interval [0, pi/2[ ∪ ]pi/2, pi] or [0°, 90°[ ∪ ]90°, 180°], there is only one α whose secant value equals sqrt6 + sqrt2. For that interval we define the function which determines the value of α as

y = arcsec(sqrt6 + sqrt2).

From the definition of arcsec(sqrt6 + sqrt2) follows that the inverse function y-1 = sec(y) = sqrt6 + sqrt2. Observe that the reciprocal function of sec(y),(sec(y))-1 is 1/sec(y) = cos(y).

Avoid misconceptions and remember (sec(y))-1 = 1/sec(y) ≠ sec-1(y) = arcsec(sqrt6 + sqrt2). And make sure to understand that the trigonometric function y=arcsec(x) is defined on a restricted domain, where it evaluates to a single value only, called the principal value:

In order to be injective, also known as one-to-one function, y = arcsec(x) if and only if sec y = x and 0 ≤ y < pi/2 or sec y = x and pi/2 < y ≤ pi. The domain of x is x ≤ −1 or 1 ≤ x.

## Conclusion

The frequently asked questions in the context include what is arcsec sqrt6 + sqrt2 degrees and what is the inverse secant sqrt6 + sqrt2 for example; reading our content they are no-brainers.

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– Article written by Mark, last updated on February 4th, 2017